On the nonlinear dynamics of a single degree of freedom oscillator with a time-varying mass

In this paper the forced vibrations of an undamped single degree of freedom oscillator with a time varying mass will be studied. An initial value problem for an oscillator equation with a Rayleigh type of nonlinearity will be formulated, and by applying a straight-forward perturbation method the problem will be solved approximately. The approximations of the solutions will be used to construct a map. By using this map the stability properties of the solutions can be determined. The stability properties of the nonlinear problem will be compared to those for the linear problem, which have been studied earlier in the literature. The instability regions in the parameter space and some phase-space figures for the nonlinear problem will be computed numerically. It will also be shown how the behaviour of the solutions changes when the instability regions in the parameter space are crossed.